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%\title{《数学写作》第一章: General Principles}
\title{Mathematical Writing \\ Chapter 1: General Principles}
%(1.1-1.2) 
%\institute{上海立信会计金融学院}
\author{NJH}
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\begin{frame}{Contents}%目录 }

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\begin{myenumerate}
\item Writing helps you to learn.
\item Writing brings out gaps in your understanding.
\item Good writing reflects clear thinking.
\item Writing is difficult. 
\item Keep your prose simple and direct.
\item To receive, and learn from, constructive criticism.
\item To read as much as you can.
\item Expository writing in mathematics that have won prizes.
\end{myenumerate}

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\begin{frame}{1.0. Quotation }

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\begin{myitemize}
\item {\bf\color{red}Good writing is clear thinking made visible.}

- Ambrose Bierce
%AMBROSE BIERCE

Write it Right: A Little Blacklist of Literary Faults (1937)

\vspace{1cm}

\item {\bf\color{red}A writer needs three qualities:

creativity, originality, clarity and a good short term memory.}

- Desmond J. Higham
%DESMOND J. HIGHAM

More Commandments of Good Writing (1992)

\end{myitemize}

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\begin{frame}{1.1. Writing helps you to learn. }

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\begin{myitemize}
\item  {\bf\color{red}Writing is not simply a task to be done once research or other preparation is completed - it can be an integral part of the work process.} 

\item  Baker explains it well [13]:

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\begin{myitemize}
\item  In writing, you clarify your own thoughts, and strengthen your conviction. Indeed, you probably grasp your thoughts for the first time. 

\item  Writing is a way of thinking. Writing actually creates thought, and generates your ability to think: you discover thoughts you hardly knew you had, and come to know what you know. 
\item  You learn as you write.
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\begin{frame}{1.2. Writing brings out gaps in your understanding. }

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\begin{myitemize}
\item Writing brings out gaps in your understanding, by forcing you to focus on steps in your thinking that you might otherwise skip. 

\item In this respect, {\bf\color{red}writing is similar to explaining your ideas to a colleague}.

\item Writing down partial research results as your work progresses can reveal structure and suggest further areas of development. 

\item Zinsser has written a delightful book that explores the idea of writing to learn [303].

\end{myitemize}

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\begin{frame}{1.3. Good writing reflects clear thinking.  }

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\begin{myitemize}
\item  It is very hard for a woolly thinker to produce clear prose. 

\item Clear thinking leads to good organization, a vital ingredient of technical writing. 

\item A well-organized piece is much easier to write than a badly organized one. 

\item If you find a particular piece difficult to write it may be because you have not found the right structure to express your ideas.

\end{myitemize}

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\begin{frame}{1.4. Writing is difficult.  }

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\begin{myitemize}

\item   Zinsser [304] says "It's one of the hardest things that people do." 

\item  It is often difficult to get started. 

\item  One solution, which works for some, is {\bf\color{red}to force yourself to write something, however clumsy it may be},
for it is often easier to modify something you have written previously than to compose from scratch.

\end{myitemize}

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\begin{frame}{1.5. To keep your prose simple and direct.  }

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\begin{myitemize}
\item  {\bf\color{red}The most fundamental tenet of technical writing is to keep your prose simple and direct. }

\item  Much of written English is unnecessarily complicated. 

\item  In writing up your research you are aiming at a relatively small audience, so it is important not to alienate part of it with long-winded or imprecise
text. 

\item  English may not be the first language of many of your readers - they, particularly, will appreciate plain writing. 

\item  Aim for economy of words. 

\item  Early drafts can usually be reduced in length substantially with consequent improvements in readability (see Chapter 7).

\end{myitemize}

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\begin{frame}{1.6. To receive, and learn from, constructive criticism.  }

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\begin{myitemize}
\item  {\bf\color{red}Probably the best way to improve your writing skills is to receive, and learn from, constructive criticism. }

\item  Ask a colleague to read and comment on your writing. 

\item  Another reader can often find errors and suggest improvements that you miss because of your familiarity with the work. 

\item  Criticism can be difficult to take, but it should be welcomed; it is a privilege to have someone else take the time to comment on your writing.

\end{myitemize}

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\begin{frame}{1.7. To read as much as you can.  }

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\begin{myitemize}
\item  {\bf\color{red}Another way to improve your writing is to read as much as you can, always with a critical eye. }

\item  In particular, I recommend perusal (the action of reading or examining something) of some of the following mathematical books. 

\item  They are by excellent writers, each of whom has his own distinctive style (this selection is inevitably biased towards my
own area of research):

\begin{myitemize}
\item   Forman S. Acton (1970), Numerical Methods That Work [3].
\item   Albert H. Beiler (1966), Recreations in the Theory of Numbers [19].
\item   David M. Burton (1980), Elementary Number Theory [44].
\item   Gene H. Golub and Charles F. Van Loan (1996), Matrix Computations [108].
\item   Paul R. Halmos (1982), A Hilbert Space Problem Book [125].
\end{myitemize}

\end{myitemize}

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\begin{myitemize}

\item  Continued: 
\begin{myitemize}
\item   {\bf\color{red}Donald E. Knuth (1973-1981), The Art of Computer Programming
[157].} (Knuth was awarded the 1986 Lerqy P. Steele Prize by the AMS for these three volumes.)
\item   Beresford N. Parlett (1998), The Symmetric Eigenvalue Problem [217].
\item   G. W. Stewart (1973), Introduction to Matrix Computations [261].
\item   Gilbert Strang (1986), Introduction to Applied Mathematics [262].
\end{myitemize}

\item   Also worth studying are papers or books that have won prizes for expository writing in mathematics. 

\item   Appendix E lists winners of the Chauvenet Prize, the Lester R. Ford Award, the George Polya Award, the Carl B. Allendoerfer Award, the Beckenbach Book Prize and the Merten M. Hasse Prize.

\end{myitemize}

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